Homology and derived series of groups

Details Homology and derived series of groups Homology and derived series of groups

2004-07-12

arxiv.org/abs/math/0407203v2

Geom. Topol. 9(2005) 2159-2191

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper49.abs.html

Scientific paper

In 1964, John Stallings established an important relationship between the low-dimensional homology of a group and its lower central series. We establish a similar relationship between the low-dimensional homology of a group and its derived series. We also define a torsion-free-solvable completion of a group that is analogous to the Malcev completion, with the role of the lower central series replaced by the derived series. We prove that the torsion-free-solvable completion is invariant under rational homology equivalence.

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